The network-hopping feature, dubbed KeepTalking, allows VoIP callers to continue a call on a voice network if they notice their WiFi or data network degrading. This solves a major problem facing many VoIP users, who want to make free or cheap calls using data networks, but who sometimes find that those networks aren’t as robust as their carrier’s voice network.

As with the original iPhone app, and Rebtel’s other apps on Android and BlackBerry, the new app lets you make free calls to other Rebtel users around the world. The company also offers extremely cheap rates for calls to international numbers.

To use the KeepTalking feature, you simply hit the appropriate button (see picture, right) while in the middle of a call. CEO Andreas Bernstrom tells me that it typically takes around two seconds for a call to switch over to a voice connection, at which point the app will use your cellular voice minutes. With KeepTalking, you’ll still be able to make free international calls to Rebtel users.

The Swedish company has spent considerable funds and effort setting up the infrastructure for its service. Bernstrom tells me it brought in $20 million worth of financing from Benchmark Capital and Index Ventures in 2006 to build a system that could connect with operators around the world and terminate voice calls in any country. Over the last nine months, the company put together the data side of its infrastructure, including codecs and stacks to carry voice over data connections.

Rebtel is the world’s second-largest mobile VoIP company (behind Skype), with 13 million connected users. The company says that 90 percent of its users make calls from its mobile apps and that it expects to hit 1 billion call minutes during 2011. It has 70 employees, most of whom are app and VoIP developers.

The company says the KeepTalking feature will reach its Android app in about a month. It’s already available on the Windows Rebtel application.